A bicycle is traveling downhill at a high speed. Suddenly, the cyclist sees that a bridge ahead has collapsed, so she has to stop. What is the maximum magnitude of acceleration the bicycle can have if it is not to flip over its front wheel—in particular, if its rear wheel is not to leave the ground? The slope makes an angle of `37^@` with the horizontal. On level ground, the centre of mass of the woman–bicycle system is at a point `1.0 m` above the ground, `1.0 m` horizontally behind the axle of the front wheel, and `35.0` cm in front of the rear axle. Assume that the tires do not skid.

Explanation

To solve the problem of determining the maximum magnitude of acceleration that a bicycle can have without flipping over its front wheel while traveling downhill, we can follow these steps:

### Step 1: Understand the forces acting on the bicycle
The bicycle is on a slope of angle \( \theta = 37^\circ \). The forces acting on the bicycle include:
- The gravitational force \( mg \) acting downward.
- The normal force \( N \) acting perpendicular to the surface of the slope.
- The frictional force \( F \) acting parallel to the slope, opposing the motion.

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